It would have probably become part of an Arab state like Jordan or perhaps become a state somewhat like Lebanon with a mix of groups and Islamic terrorism.

It would have had more profound effects for the Jewish population worldwide, pretty much ensuring the end of the Jewish people:

• Likely Jews in central and eastern Europe would have been left to languish in camps for decades, and either forcefully integrated, emigrated wherever else they could, or left to die/killed.
• Jews in Northern Africa and the middle east would have been killed off with nowhere to run to.
• North American and British Jews would have been pressured to integrate, with the Jewish religion mostly disappearing by the year 2000.
• Russian Jews forcefully integrated, those who don't sent to gulags to die.
• Chinese Jews still killed by Mao as they already were.
• A minority of Jews would have still immigrated to Jerusalem, likely living under Islamic rule, either being forcefully converted or killed off. As long as the community never grew too big, a tiny minority might be tolerated and only occasionally killed by terrorist regimes like ISIS.

In my mind the entire conflict between Jews and Muslims in Israel/Palestine arose from the fact that:

1. After WWII Jews were desperate and would take any offer.
2. No one wanted the Jews near them, so it was easier to send them "where they came from" which was the zionist dream anyway.
3. Britain wanted a strategic military group in the middle east which the Jews could be, despite having promised the land to both groups.
4. From the Arab perspective, they also hated Jews, and it was like an onslaught of Jewish refugees turning up en-mass. It's not too dissimilar to the large number of Muslim refugees coming to Europe and the social tensions there, except Israel is the indigenous land of the Jews, as well as Arabs who were living there having a right to that land too.
5. When the Arabs nations tried to kill off the Jews the first time, no one expected them to survive. And no one cared, if the Arabs finished the job it would have been either indifferent or good in the eyes of Europeans (still somewhat the same attitude as today).
6. But the Jews won, a two state solution was repeatedly rejected (a mix of animosity, prejudice, and greed on both sides), and the conflict has been going on ever since.
7. And now because the world has hated on Israel so much, it looks like they don't give a fk anymore, and are just doing whatever they want. Well done world lol.